Let the life of the original be x, and x obeys the exponential distribution with parameter λ. Then the density function of x is as follows:

The expected ex = 1/λ of x can be known from the density function. Variance dx = 1/(λ 2)?

Now Ex= 100, λ =1100. So DX = 10000.

Xi is randomly sampled from the whole exponential distribution, so Xi also obeys the exponential distribution of λ =1100, so E (Xi) = 100, and D (Xi) = 10000.

P {σ Xi > 1920}=？

Let y = σ xi, and y ~γ(2n, n/λ) can be calculated. In this problem, n = 16? λ= 1/ 100。

p {σXi & gt； 1920 } = P { Y & gt； 1920}=∫Gamma(2n，n/λ) dt？ The integer domain of t is (1920, +∞).

The distribution of y calculated by p.s. can be obtained by calculating the moment generating function.